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Version 8.1 von Frauke Beckstette am 2024/12/18 13:42
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1 {{formula}} f(x)=e^x+2 {{/formula}}
2 globales Verhalten:
3 wenn {{formula}} x \to -\infty{{/formula}} dann {{formula}} f(x) \to y=2 {{/formula}}
4 wenn {{formula}} x \to \infty{{/formula}} dann {{formula}} f(x) \to \infty {{/formula}}
5 Asymptote: {{formula}} y=2 {{/formula}}
6 Schnittpunkt mit der {{formula}}y{{/formula}}-Achse: {{formula}} S_y(0|3) {{/formula}}
7 [[image:Skizze1.png||width="400"]]
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10 {{formula}} g(x)=e^{-x} - 1,5 {{/formula}}
11 globales Verhalten:
12 wenn {{formula}} x \to -\infty{{/formula}} dann {{formula}} f(x) \to \infty {{/formula}}
13 wenn {{formula}} x \to \infty{{/formula}} dann {{formula}} f(x) \to y=-1,5 {{/formula}}
14 Asymptote: {{formula}} y=2 {{/formula}}
15 Schnittpunkt mit der {{formula}}y{{/formula}}-Achse: {{formula}} S_y(0|-0,5) {{/formula}}
16 [[image:Skizze2.png||width="400"]]
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19 {{formula}} h(x)=-e^{x+2,5} {{/formula}}
20 globales Verhalten:
21 wenn {{formula}} x \to -\infty{{/formula}} dann {{formula}} f(x) \to y=0 {{/formula}}
22 wenn {{formula}} x \to \infty{{/formula}} dann {{formula}} f(x) \to -\infty {{/formula}}
23 Asymptote: {{formula}} y=2 {{/formula}}
24 Schnittpunkt mit der {{formula}}y{{/formula}}-Achse: {{formula}} S_y(0|-e^{2,5}) {{/formula}}
25 [[image:Skizze3.png||width="400"]]